8x^2=90x+182

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Solution for 8x^2=90x+182 equation:


Simplifying
8x2 = 90x + 182

Reorder the terms:
8x2 = 182 + 90x

Solving
8x2 = 182 + 90x

Solving for variable 'x'.

Reorder the terms:
-182 + -90x + 8x2 = 182 + 90x + -182 + -90x

Reorder the terms:
-182 + -90x + 8x2 = 182 + -182 + 90x + -90x

Combine like terms: 182 + -182 = 0
-182 + -90x + 8x2 = 0 + 90x + -90x
-182 + -90x + 8x2 = 90x + -90x

Combine like terms: 90x + -90x = 0
-182 + -90x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-91 + -45x + 4x2) = 0

Factor a trinomial.
2((-7 + -4x)(13 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-7 + -4x)' equal to zero and attempt to solve: Simplifying -7 + -4x = 0 Solving -7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4x = 0 + 7 -4x = 0 + 7 Combine like terms: 0 + 7 = 7 -4x = 7 Divide each side by '-4'. x = -1.75 Simplifying x = -1.75

Subproblem 2

Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13

Solution

x = {-1.75, 13}

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